Sounds like your body is changing, even though scale is not. That's ok, because you're actually getting to what you want - reducing fat. I would recommend you to take measurements of yourself in several places (neck, arms, thighs, hips, waist, etc) and measure yourself once a month. You will know that you're dropping inches. Since walking 6 miles became a piece of cake for you, your body is used to this workout by now. I think you should change it up, and give your body a challenge. Try bycicling, jogging/running as an interval training for those 6 miles, do some weight training if you don't do it yet. You may also cut your calories to 1400-1300 for a week or two.
While I don't know for sure, but chemicals in diet coke may effect your body in a way that hinders weight loss. Drinking a lot of that stuff is bad for your health anyway, so if you aim at reducing diet soda and increasing your water intake, that may help too.
hope you'll break that plato soon!